Improper ferroelectricity (trimerization) in the hexagonal manganites RMnO 3 leads to a network of coupled structural and magnetic vortices that induce domain wall magnetoelectricity and magnetization (M), neither of which, however, occurs in the bulk. Here we combine first-principles calculations, group-theoretic techniques and microscopic spin models to show how the trimerization not only induces a polarization (P) but also a bulk M and bulk magnetoelectric (ME) effect. This results in the existence of a bulk linear ME vortex structure or a bulk ME coupling such that if P reverses so does M. To measure the predicted ME vortex, we suggest RMnO 3 under large magnetic field. We suggest a family of materials, the hexagonal RFeO 3 ferrites, also display the predicted phenomena in their ground state.

The discovery of superconductivity in LaFeAsO introduced the ferropnictides as a major new class of superconducting compounds with critical temperatures second only to cuprates. The presence of magnetic iron makes ferropnictides radically different from cuprates. Antiferromagnetism of the parent compounds strongly suggests that superconductivity and magnetism are closely related. However, the character of magnetic interactions and spin fluctuations in ferropnictides, in spite of vigorous efforts, has until now resisted understanding within any conventional model of magnetism. Here we show that the most puzzling features can be naturally reconciled within a rather simple effective spin model with biquadratic interactions, which is consistent with electronic structure calculations. By going beyond the Heisenberg model, this description explains numerous experimentally observed properties, including the peculiarities of the spin wave spectrum, thin domain walls, crossover from first to second order phase transition under doping in some compounds, and offers new insight in the occurrence of the nematic phase above the antiferromagnetic phase transition.Comment: 5 pages, 3 figures, revtex

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The electronic structure and magnetism of chromia ͑corundum-type Cr 2 O 3 ͒ are studied using full-potential first-principles calculations. The electronic correlations are included within the LSDA+ U method. The energies of different magnetic configurations are very well fitted by the Heisenberg Hamiltonian with strong exchange interaction with two nearest neighbors and additional weak interaction up to the fifth neighbor shell. These energies are insensitive to the position of the oxygen states, indicating that magnetism in Cr 2 O 3 is dominated by direct exchange. The Néel temperature is calculated using the pair-cluster approximation for localized quantum spins of magnitude 3/2. Very good agreement with experiment is found for all properties including the equilibrium volume, spectral density, local magnetic moment, band gap, and the Néel temperature for the values of U and J that are close to those obtained within the constrained occupation method. The band gap is of the Mott-Hubbard type.

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